α-B-splines non-stationary subdivision schemes for grids of arbitrary topology design

This paper proposes a new class of B-spline-like functions that blend trigonometric and hyperbolic functions. A new family of non-stationary subdivision schemes of order k >= 3 has been built using the refinement of these B-splines. The schemes yield a Ck-2 limit curve that represents the spline. A tensorproduct subdivision approach is used to produce a limit surface from an initial mesh with regular vertices. For extraordinary vertices, new rules are proposed. Except at extraordinary points, where they are C-1 continuous, the scheme generates Ck-2 continuous limit surfaces. The proposed scheme is a particular case of many well-known curve and surface subdivision schemes. Some examples are given to demonstrate how well the new schemes perform in generating various shapes of limit curves and surfaces. (C) 2022 Elsevier Ltd. All rights reserved.